Answer: The largest product we can get is: 26244
How many possible sets are there the sum of whose elements is 28?
Infinite, since one can always take negative integers to cancel the extra sum due to positive integers.
We know that for 28,
(k-2)*2 <= k
2k-4 <= k
k <= 4
So, we should only consider numbers less than or equal to 4.
Now, 4 can be replaced by 2*2 and there is no point in taking 1 since it will not increase product result.
So, we are left with 2 and 3. Some possible solutions are:
{3,3,3,3,3,3,3,3,2,2} or {3,3,3,3,3,3,2,2,2,2,2} etc.
Out of all these, the maximum product we can get is from {3,3,3,3,3,3,3,3,2,2} which is: 26244
So, The largest product we can get is: 26244
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